"We asked for flexibility on how the federal money is passed down to the states and the cuts that are passed down, that we could have some flexibility to do what's in the best interest of our states," said Oklahoma Gov. Mary Fallin, a Republican.

The governors said they were not endorsing any particular proposal but said they wanted to share their ideas on ways that states could play a role in helping reduce the deficit. The governors were meeting later in the day with congressional leaders and said they planned to work with Vice President Joe Biden in the coming weeks.

The Republican proposal Monday sparked a predictable round of partisanship.

"To protect the middle class while reducing the deficit, simple math dictates that tax rates must rise on the top 2 percent of taxpayers next year," Senate Majority Leader Harry Reid, D-Nev., said in a statement. "The sooner Republicans grasp that reality, the sooner we can avoid the fiscal cliff."

The fiscal cliff is a combination of expiring Bush-era tax cuts and automatic, across-the-board spending cuts due to take effect in January. The cliff is a result of prior failures of Congress and Obama to make a budget deal.

The GOP proposal itself revives a host of ideas from failed talks with Obama in the summer of 2011. Then, Obama was willing to discuss politically risky ideas such as raising the eligibility age for Medicare, implementing a new inflation adjustment for Social Security cost-of-living adjustments and requiring wealthier Medicare recipients to pay more for their benefits.

By GOP math, the plan would produce more than $2 trillion in budget savings over the coming decade: $800 billion in higher taxes; $600 billion in savings from costly health care programs like Medicare; $300 billion from other proposals such as forcing federal workers to contribute more toward their pensions; and $300 billion in additional savings from the Pentagon budget and domestic programs funded by Congress each year.

Last week, the White House delivered to Capitol Hill its opening proposal: $1.6 trillion in higher taxes over a decade, a possible extension of the temporary Social Security payroll tax cut and heightened presidential power to raise the national debt limit without the approval of Congress.

In exchange, the president would back $600 billion in spending cuts, including $350 billion from Medicare and other health programs. But he also wants $200 billion in new spending for jobless benefits, public works projects and aid for struggling homeowners. His proposal for raising the ceiling on government borrowing would make it virtually impossible for Congress to block him going forward.

Other participants in the Tuesday meeting between Obama and the governors included Republicans Gary Herbert of Utah and Scott Walker of Wisconsin and Democrats Mike Beebe of Arkansas and Mark Dayton of Minnesota.